Maxwell-Stefan diffusion asymptotic for gas mixtures in non-isothermal setting

TL;DR

This paper derives a coupled Maxwell-Stefan diffusion and temperature model for gas mixtures from Boltzmann equations, extending classical diffusion models to non-isothermal conditions through asymptotic analysis.

Contribution

It introduces a novel coupled system linking diffusion and temperature for gas mixtures, derived rigorously from first principles.

Findings

Derivation of a coupled diffusion-temperature model from Boltzmann equations.

Asymptotic analysis under diffuse scaling validates the model.

Extension of classical Maxwell-Stefan diffusion to non-isothermal settings.

Abstract

A mathematical model is proposed where the classical Maxwell-Stefan diffusion model for gas mixtures is coupled to an advection-type equation for the temperature of the physical system. This coupled system is derived from first principles in the sense that the starting point of our analysis is a system of Boltzmann equations for gaseous mixtures. We perform an asymptotic analysis on the Boltzmann model under diffuse scaling to arrive at the proposed coupled system.